Many real-world engineering optimization problems usually need a lot of time for function evaluations or have massive decision variables. It is still a big challenge to address these problems effectively. Recently, surrogate-assisted meta-heuristic algorithms have drawn increasing attention, and have shown their potential to deal with such expensive complex optimization problems. In this study, a surrogate-assisted quasi-affine transformation evolutionary (SA-QUATRE) algorithm is proposed to further enhance the optimization efficiency and effectiveness. In SA-QUATRE, the global and the local surrogate models are effectively combined for fitness estimation. The global surrogate model is built based on all data in the database for global exploration. While, the local surrogate model is constructed with a predefined number of top best samples for local exploitation. Meanwhile, both the generation- and individual-based evolution controls as well as a top best restart strategy are incorporated in the global and the local searches. To enhance the exploration and the exploitation capabilities, the global search uses the mean of the population to be evaluated with the expensive real fitness function, while the local search chooses the individual with the best fitness according to the surrogate for real evaluation. The proposed SA-QUATRE is compared with five state-of-the-art optimization approaches over seven commonly used benchmark functions with dimensions varying from 10 to 100. Moreover, the proposed SA-QUATRE is also applied to solve the tension/compression spring design problem. The experimental results show that SA-QUATRE is promising for optimizing computationally expensive problems.

许多现实世界中的工程优化问题通常需要大量时间进行功能评估或拥有大量决策变量。有效解决这些问题仍然是一个巨大的挑战。近来，代理辅助的元启发式算法引起了越来越多的关注，并显示出了其解决此类昂贵的复杂优化问题的潜力。本文提出了一种代理辅助的仿射仿射变换进化算法（SA-QUATRE），以进一步提高优化效率和有效性。在SA-QUATRE中，可以将全局和局部代理模型有效地结合起来进行适合度估计。全局代理模型是基于数据库中的所有数据构建的，用于全局浏览。而，本地代理模型是使用预定义数量的用于本地开发的最佳样本构建的。同时，基于生成和基于个人的演化控制以及最佳的重新启动策略都被并入了全局和本地搜索中。为了增强勘探和开发能力，全局搜索使用具有昂贵的真实适应度函数的待评估人口平均值，而本地搜索会根据替代对象选择适应度最高的个体进行真实评估。将拟议的SA-QUATRE与七个最常用的基准函数（在10到100之间变化）的五个最新优化方法进行了比较。此外，拟议的SA-QUATRE还用于解决拉伸/压缩弹簧的设计问题。